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    <p>The lookaheads used in an LR(1) parser are computed as follows. First, the start state has an item of the form</p> <pre><code>S -&gt; .w ($) </code></pre> <p>for every production S -> w, where S is the start symbol. Here, the $ marker denotes the end of the input.</p> <p>Next, for any state that contains an item of the form A -> x.By (t), where x is an arbitrary string of terminals and nonterminals and B is a nonterminal, you add an item of the form B -> .w (s) for every production B -> w and for every terminal in the set FIRST(yt). (Here, FIRST refers to <a href="http://www.cs.virginia.edu/~cs415/reading/FirstFollowLL.pdf">FIRST sets</a>, which are usually introduced when talking about LL parsers. If you haven't seen them before, I would take a few minutes to look over those lecture notes).</p> <p>Let's try this out on your grammar. We start off by creating an item set containing</p> <pre><code>S -&gt; .AB ($) </code></pre> <p>Next, using our second rule, for every production of A, we add in a new item corresponding to that production and with lookaheads of every terminal in FIRST(B$). Since B always produces the string d, FIRST(B$) = d, so all of the productions we introduce will have lookahead d. This gives</p> <pre><code>S -&gt; .AB ($) A -&gt; .aAb (d) A -&gt; .a (d) </code></pre> <p>Now, let's build the state corresponding to seeing an 'a' in this initial state. We start by moving the dot over one step for each production that starts with a:</p> <pre><code>A -&gt; a.Ab (d) A -&gt; a. (d) </code></pre> <p>Now, since the first item has a dot before a nonterminal, we use our rule to add one item for each production of A, giving those items lookahead FIRST(bd) = b. This gives</p> <pre><code>A -&gt; a.Ab (d) A -&gt; a. (d) A -&gt; .aAb (b) A -&gt; .a (b) </code></pre> <p>Continuing this process will ultimately construct all the LR(1) states for this LR(1) parser. This is shown here:</p> <pre><code>[0] S -&gt; .AB ($) A -&gt; .aAb (d) A -&gt; .a (d) [1] A -&gt; a.Ab (d) A -&gt; a. (d) A -&gt; .aAb (b) A -&gt; .a (b) [2] A -&gt; a.Ab (b) A -&gt; a. (b) A -&gt; .aAb (b) A -&gt; .a (b) [3] A -&gt; aA.b (d) [4] A -&gt; aAb. (d) [5] S -&gt; A.B ($) B -&gt; .d ($) [6] B -&gt; d. ($) [7] S -&gt; AB. ($) [8] A -&gt; aA.b (b) [9] A -&gt; aAb. (b) </code></pre> <p>In case it helps, I taught a compilers course last summer and have <strong><a href="http://www.stanford.edu/class/archive/cs/cs143/cs143.1128/">all the lecture slides available online</a></strong>. The slides on bottom-up parsing should cover all of the details of LR parsing and parse table construction, and I hope that you find them useful!</p> <p>Hope this helps!</p>
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    1. COThank you. Can you explain why $ is included in the lookahead sets in the following grammar, but it's not in FIRST($A) ? S → •A {$} A → • AA {$, b} A → • bc {$ ,b }
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    2. CO@mrjasmin- I need to see more of the grammar to know what the FIRST and lookahead sets should be; can you post more? Also, note that you shouldn't be computing FIRST($A) anywhere. If you have A -> .AA ($), the lookaheads for the resulting items would be the terminals in FIRST(A$), not FIRST($A). Does that help at all?
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    3. COHi ! This question is from an exam and all that is given is: S -> .A {$} A -> .AA { } A -> .bc { } The student is supposed to find the lookahead set- And the answer is the post above. I don't understand how $ is a lookahead
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